Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in Lévy models

ArXiv ID: 2312.03915 “View on arXiv”

Authors: Unknown

Abstract

We analyze the qualitative differences between prices of double barrier no-touch options in the Heston model and pure jump KoBoL model calibrated to the same set of the empirical data, and discuss the potential for arbitrage opportunities if the correct model is a pure jump model. We explain and demonstrate with numerical examples that accurate and fast calculations of prices of double barrier options in jump models are extremely difficult using the numerical methods available in the literature. We develop a new efficient method (GWR-SINH method) based of the Gaver-Wynn-Rho acceleration applied to the Bromwich integral; the SINH-acceleration and simplified trapezoid rule are used to evaluate perpetual double barrier options for each value of the spectral parameter in GWR-algorithm. The program in Matlab running on a Mac with moderate characteristics achieves the precision of the order of E-5 and better in several several dozen of milliseconds; the precision E-07 is achievable in about 0.1 sec. We outline the extension of GWR-SINH method to regime-switching models and models with stochastic parameters and stochastic interest rates.

Keywords: Double barrier options, KoBoL model, Gaver-Wynn-Rho acceleration, SINH-acceleration, Regime-switching models, Equity Derivatives

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper uses advanced mathematics including Wiener-Hopf factorization, Laplace transforms, and a new GWR-SINH acceleration algorithm, placing it at the high end of math complexity. Empirical rigor is moderate to high, with calibration to real data, backtest-ready numerical examples, and precise performance metrics (e.g., ms-level computation, E-5 to E-7 precision).

  flowchart TD
    A["Research Goal: Analyze Heston vs. KoBoL for<br>Double Barrier Options & Arbitrage"] --> B["Data & Calibration"]
    B --> C["Computational Challenge:<br>High difficulty in jump models"]
    C --> D["Methodology: GWR-SINH Method"]
    D --> E["Process: Gaver-Wynn-Rho +<br>SINH-Acceleration"]
    E --> F["Findings: Precise E-5 error in<br>milliseconds; Arbitrage potential"]
    
    style A fill:#f9f,stroke:#333,stroke-width:2px
    style F fill:#9f9,stroke:#333,stroke-width:2px